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the ambiguity is that it's presented as something the host does in this particular instance, but the validity of the probability calculations depends on it being a protocol the host always follows (in particular, that the host will always reveal one of the goats not behind the contestant's first choice of doors).

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There is no "always follows". This is an event which will not be repeated in the history of the world. All there is is 3 doors: you pick one, the host opens another door which contains a goat, and offers you a choice. Why he picked the door that he chose is irrelevant. All that is relevant is that (a) it's not the door you chose, and (b) it contains a goat. You don't need anything beyond that to solve this problem. If you think you need something beyond that to solve the problem, you're not solving it correctly.

"Why he picked the door that he chose is irrelevant" I disagree. If he picked the door at random and it just happened to contain a goat it's 50/50. If he picked the door because he was always going to pick that door if it contained a goat then it's 50/50

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